Traffic Assignment Using a Density-Based Travel-Time Function for Intelligent Transportation Systems

This paper presents and shows why density-based travel-time function is consistent with the fundamental diagram from traffic theory and then reviews the applications of travel time in intelligent transportation systems. This paper presents a density-based travel-time function that does not have the ill-posedness that is present in flow-based travel-time functions. The classic steady-state traffic assignment is cast using this new travel-time function, and corresponding mathematical programming formulations are proposed. It is shown that the modified Beckman formulation based on the density-based travel-time function provides a unique solution for link flows and link densities where the Wardrop condition has nonunique values for arc traffic densities.